You could talk to your users... (i.e. UX research), observe them using your website or product and ask them non leading probing questions to see what the intent is behind the behaviors affecting your bottom line. Qualitative research methods are a rich source of insight that is typically underinvested and underutilized.
Analytics (quantitative data) can help you find areas of bottlenecks to explore further by doing qualitative user research and getting to the ‘why’ behind the people problems standing in the way of your metrics you are tracking (retention, adoption, etc.). This is called ‘triangulation’ using quant and qual research methods to understand your users more deeply than just looking at data can achieve.
This is a very important point, thanks for saying this. It’s amazing how many people think they can start an indie SaaS and think that all they have to do is build it, deploy it, and buy AdWords or whatever. Talking to your customers is more important than any of that, and it’s fun.
UX research participants are usually compensated, and so it's usually done to drill down deeper into problems that analytics found and test possible explainations. I don't see what's unscientific about that.
Analytics (quantitative data) can help you find areas of bottlenecks to explore further by doing qualitative user research and getting to the ‘why’ behind the people problems standing in the way of your metrics you are tracking (retention, adoption, etc.). This is called ‘triangulation’ using quant and qual research methods to understand your users more deeply than just looking at data can achieve.